The Mathematics of GeoEnergy

ITCZ

In Chapter 12 of the book, we discuss tropical instability waves (TIW) of the equatorial Pacific as the higher wavenumber (and higher frequency) companion to the lower wavenumber ENSO (El Nino /Southern Oscillation) behavior. Sutherland et al have already published several papers this year that appear to add some valuable insight to the mathematical underpinnings to the fluid-mechanical relationship.

“It is estimated that globally 1 TW of power is transferred from the lunisolar tides to internal tides[1]. The action of the barotropic tide over bottom topography can generate vertically propagating beams near the source. While some fraction of that energy is dissipated in the near field (as observed, for example, near the Hawaiian Ridge [2]), most of the energy becomes manifest as low-mode internal tides in the far field where they may then propagate thousands of kilometers from the source [3]. An outstanding question asks how the energy from these waves ultimately cascades from large to small scale where it may be dissipated, thus closing this branch of the oceanic energy budget. Several possibilities have been explored, including dissipation when the internal tide interacts with rough bottom topography, with the continental slopes and shelves, and with mean flows and eddies (for a recent review, see MacKinnon et al. [4]). It has also been suggested that, away from topography and background flows, internal modes may be dissipated due to nonlinear wave-wave interactions including the case of triadic resonant instability (hereafter TRI), in which a pair of “sibling” waves grow out of the background noise field through resonant interactions with the “parent” wave”